Eric Pickles plans to bring people together for lunch and for community music events. Photograph: Dave Thompson/PA

The centrepiece of Eric Pickles's long-awaited strategy to promote community integration has emerged: a Big Lunch in which people sit down and eat with their neighbours.

Pickles is also keen to encourage a national community music day on 9 September in which communities can come together through choral singing in shopping centres, steel drum bands in park bandstands and piano recitals in schools.

The Big Lunch is described as "encouraging people to interact by sitting down and having lunch with their neighbours, helping to build stronger communities and develop the local resources to overcome tensions and conflicts".

More than 2.4 million people took part in a 2011 Big Lunch which was initiated by the Eden Project and Pickles hopes to bring even more people together on Sunday 3 June this year – the same weekend as the Queen's diamond jubilee celebrations.

"Britain is a place where the vast majority of people from all walks of life get on well with each other. Events such as the royal wedding and the Big Lunch show that community spirit is thriving," said Pickles on Tuesday. "I welcome the contribution of everyone but those who advocate separate lives are wrong. It is time to concentrate on the things that unite the British people."

The communities secretary is also reported to be pressing ahead with his plan for a curry college to train British people from all backgrounds to become chefs and wants to develop it further with "cordon bleu" scholarships.

The integration strategy document promises renewed efforts to "outflank extremism", including a national group to help local communities deal with protests by the English Defence League, Muslims Against Crusades and other extreme groups, and a working group on anti-Muslim hate crime.

But it also adopts a minimalist approach to the official encouragement of "community cohesion" saying that in future government will only act exceptionally.

Instead of community cohesion grants only small amounts of official funding will be made available to "kick-start action" with special "integration projects" now seen as too often proving irrelevant to daily lives or unsustainable.

There is also an emphasis on providing additional funding for English language classes only for those who are not in work and unable to afford fees themselves, such as women with children living in closed communities.

But the delayed 26-page strategy, which only applies to England, does not live up to its billing in some newspapers as a major break with Labour's policies in this area. There is no wholesale rejection of multiculturalism and no mention of dropping Whitehall diversity targets.

The strategy does say that in the past integration challenges have been met with legal rights and obligations around equalities, discrimination and hate crime and that this approach has not solved the problem and may, in some cases, have exacerbated it by singling out specific groups for special treatment.

It adds that ministers expect mainstream public services to make the most impact on integration rather than any specific new official integration activity.

They will move away from a "Whitehall-dictated approach" to encouraging collective local action such as the Big Lunch and the community music day instead.

The communities department has been pressing ahead with non-controversial elements such as the national citizen service, which will bring together 30,000 young people of different backgrounds this year, and a Year of Service, which is a series of special volunteering days throughout the diamond jubilee.

The race equality thinktank Runnymede described the new strategy as a "dangerous and ill-advised reversion to assimilationist policy". Its director, Dr Rob Berkeley, said it subsumed all the differences of ethnicity and heritage into a majoritarian "mainstream".

"The secretary of state appears to have completely misunderstood the problems we face in building a successful multi-ethnic society, and the solutions proposed as a result simply miss the point. This government has sought to make fairness its catchword; this strategy does nothing to turn such rhetoric into reality," he said.

Sunder Katwala of British Future said the risk in the strategy was that while the government spoke clearly about integration, it was retreating to doing less about it. "The local matters and so does personal responsibility, but an argument that national government will act 'only exceptionally' is too hands-off and hollows out what government needs to do to break down barriers. Integration is a two-way street," he said.

"There is good evidence that well-designed projects to support integration – for example in the English language – are effective and cost-effective.

"As the government rightly sets out why integration matters, it must not duck its own role in helping to achieve it."